\relax 
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Separabilidad por c\IeC {\'\i }rculos entre pol\IeC {\'\i }gonos convexos}{47}{chapter.3}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Nuestro problema}{47}{section.3.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Separabilidad por c\IeC {\'\i }rculos entre conjuntos de puntos.}}{47}{figure.3.1}}
\newlabel{F_CircularSeparability}{{3.1}{47}{\small Separabilidad por círculos entre conjuntos de puntos}{figure.3.1}{}}
\citation{ComputingCircularSeparability}
\@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip Separabilidad por c\IeC {\'\i }rculos entre pol\IeC {\'\i }gonos convexos.}}{49}{figure.3.2}}
\newlabel{F_CircularPolygonSeparability}{{3.2}{49}{\small Separabilidad por círculos entre polígonos convexos}{figure.3.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}C\IeC {\'\i }rculos separadores}{49}{section.3.2}}
\newlabel{centroEnV(P)}{{3.2.2}{50}{Círculos separadores\relax }{tma.3.2.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.3}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip En esta figura se observa la prueba de la Observaci\IeC {\'o}n~\ref  {centroEnV(P)}.}}{51}{figure.3.3}}
\newlabel{F_centroEnV(P)}{{3.3}{51}{\small En esta figura se observa la prueba de la Observación~\ref {centroEnV(P)}}{figure.3.3}{}}
\newlabel{AncestroComun}{{3.2.3}{51}{Círculos separadores\relax }{tma.3.2.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.4}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip En esta figura se observa la prueba de la Proposici\IeC {\'o}n~\ref  {AncestroComun}.}}{52}{figure.3.4}}
\newlabel{F_AncestroComun}{{3.4}{52}{\small En esta figura se observa la prueba de la Proposición~\ref {AncestroComun}}{figure.3.4}{}}
\newlabel{AncestroSeparadorGral}{{3.2.4}{52}{Círculos separadores\relax }{tma.3.2.4}{}}
\newlabel{c en T_s}{{3.2.5}{53}{Círculos separadores\relax }{tma.3.2.5}{}}
\newlabel{obs:CcTangentToQ}{{3.2.6}{53}{Círculos separadores\relax }{tma.3.2.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.3}El algoritmo}{53}{section.3.3}}
\citation{ComputingExtremeDistancesBetweenConvexPolygons}
\@writefile{lof}{\contentsline {figure}{\numberline {3.5}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip La construcci\IeC {\'o}n del punto $s_0$.}}{54}{figure.3.5}}
\newlabel{F_ConstruccionS_0}{{3.5}{54}{\small La construcción del punto $s_0$}{figure.3.5}{}}
\citation{ComputingExtremeDistancesBetweenConvexPolygons}
\newlabel{Alg busqueda c}{{3.3.1}{55}{El algoritmo\relax }{alg.3.3.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.6}{\ignorespaces El segmento $S$ sobre el cual se encuentra $c$.}}{55}{figure.3.6}}
\newlabel{F_SegmentoS}{{3.6}{55}{El segmento $S$ sobre el cual se encuentra $c$}{figure.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.1}Precisando la posici\IeC {\'o}n de $c$}{56}{subsection.3.3.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.7}{\ignorespaces La construcci\IeC {\'o}n del conjunto $Q_S$ y el punto $q_c$.}}{56}{figure.3.7}}
\newlabel{F_ConstruccionQ_S}{{3.7}{56}{La construcción del conjunto $Q_S$ y el punto $q_c$}{figure.3.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.8}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip La maximalidad de $q_{c}$ bajo la funci\IeC {\'o}n $\tau $.}}{57}{figure.3.8}}
\newlabel{fig:TauEsUnimodal}{{3.8}{57}{\small La maximalidad de $q_{c}$ bajo la función $\tau $}{figure.3.8}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.9}{\ignorespaces \relax \fontsize  {10.95}{13.6}\selectfont  \abovedisplayskip 11\p@ plus3\p@ minus6\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 5\p@ plus2.5\p@ minus\p@ \topsep 10\p@ plus4\p@ minus6\p@ \itemsep 5\p@ plus2.5\p@ minus\p@ {\leftmargin \leftmargini \topsep 9\p@ plus3\p@ minus5\p@ \parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip {Ya que el c\IeC {\'\i }rculo $C(u)$ intersecta a $Q$ en m\IeC {\'a}s de dos puntos, $\tau (x)$ no es unimodal cuando la definimos sobre toda la frontera de $Q$, sin embargo lo es cuando la definimos sobre $Q_S$.}}}{58}{figure.3.9}}
\newlabel{fig:NotUnimodalInAllQ}{{3.9}{58}{\small {Ya que el círculo $C(u)$ intersecta a $Q$ en más de dos puntos, $\tau (x)$ no es unimodal cuando la definimos sobre toda la frontera de $Q$, sin embargo lo es cuando la definimos sobre $Q_S$.}\relax }{figure.3.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3.2}Algoritmo para encontrar $q_{c}$}{58}{subsection.3.3.2}}
\@setckpt{cap3}{
\setcounter{page}{61}
\setcounter{equation}{2}
\setcounter{enumi}{0}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{0}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{3}
\setcounter{section}{3}
\setcounter{subsection}{2}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{9}
\setcounter{table}{0}
\setcounter{parentequation}{0}
\setcounter{Item}{21}
\setcounter{Hfootnote}{1}
\setcounter{section@level}{2}
\setcounter{defi}{8}
\setcounter{tma}{1}
\setcounter{alg}{2}
}
